Nuprl Lemma : rsum-shift
∀[k,n,m:ℤ]. ∀[x:Top]. (Σ{x[i] | n≤i≤m} ~ Σ{x[i + k] | n - k≤i≤m - k})
Proof
Definitions occuring in Statement :
rsum: Σ{x[k] | n≤k≤m},
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
subtract: n - m,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rsum: Σ{x[k] | n≤k≤m},
has-value: (a)↓,
uimplies: b supposing a,
compose: f o g,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtract: n - m,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
sq_type: SQType(T),
guard: {T}
Latex:
\mforall{}[k,n,m:\mBbbZ{}]. \mforall{}[x:Top]. (\mSigma{}\{x[i] | n\mleq{}i\mleq{}m\} \msim{} \mSigma{}\{x[i + k] | n - k\mleq{}i\mleq{}m - k\})
Date html generated:
2020_05_20-AM-11_11_18
Last ObjectModification:
2019_12_28-PM-09_01_21
Theory : reals
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